Abstract

In this article, a technique is proposed for obtaining better and accurate results for nonlinear PDEs. We constructed abundant exact solutions via exp\( ( - \varphi \left( \eta \right)) \)-expansion method for the Zakharov–Kuznetsov-modified equal-width (ZK-MEW) equation and the (2 + 1)-dimensional Burgers equation. The traveling wave solutions are found through the hyperbolic functions, the trigonometric functions and the rational functions. The specified idea is very pragmatic for PDEs, and could be extended to engineering problems.

Conclusions

The exp\( ( - \varphi \left( \eta \right)) \)-expansion method has been successfully applied to find the exact solutions of (ZK-MEW) equation and the Burger’s equation. The attained results show that the proposed technique is effective and capable for solving nonlinear partial differential equations. In this study, some exact solitary wave solutions, mostly solitons and kink solutions, are obtained through the hyperbolic and rational functions. This study shows that the proposed method is quite proficient and practically well organized in finding exact solutions of other physical problems.

Declarations

Authors’ contributions

The work was carried out in cooperation among all the authors (STM-D, AA and MAI). All authors have a good involvement to plan the paper, and to execute the analysis of this research work together. All authors read and approved the final manuscript.

Compliance with ethical guidelines

Competing interests The authors declare that they have no competing interests.

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors’ Affiliations

(1)

Department of Mathematics, Faculty of Sciences, HITEC University Taxila